Computation of time optimal control problems governed by linear ordinary differential equations
The computation of the optimal time for a time optimal control problem governed by a system of linear ordinary differential equations is approached by transforming the problem into an equivalent norm optimal control problem. Properties of the two problems are extensively studied: bang-bang type principle, equivalence property, first-order necessary and sufficient condition. A bisection based root finding algorithm to compute the optimal time is elaborated by solving a sequence of norm optimal control problems and their Lagrangian dual problems. The convergence of the optimal norm is proved. An iteratively reweighted least squares method is described in order to solve the nonsmooth Lagrangian dual optimization problem. The efficiency of the proposed numerical algorithm is shown by means of a few practical examples.
scientific article; zbMATH DE number 6818457
scientific article